{"title":"Growth rate of liquidity provider's wealth in G3Ms","authors":"Cheuk Yin Lee, Shen-Ning Tung, Tai-Ho Wang","doi":"arxiv-2403.18177","DOIUrl":null,"url":null,"abstract":"Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent\na widely used class of automated market makers (AMMs). These G3Ms are\ncharacterized by the following rule: the reserves of the AMM must maintain the\nsame (weighted) geometric mean before and after each trade. This paper\ninvestigates the effects of trading fees on liquidity providers' (LP)\nprofitability in a G3M, as well as the adverse selection faced by LPs due to\narbitrage activities involving a reference market. Our work expands the model\ndescribed in previous studies for G3Ms, integrating transaction fees and\ncontinuous-time arbitrage into the analysis. Within this context, we analyze\nG3M dynamics, characterized by stochastic storage processes, and calculate the\ngrowth rate of LP wealth. In particular, our results align with and extend the\nresults concerning the constant product market maker, commonly referred to as\nUniswap v2.","PeriodicalId":501478,"journal":{"name":"arXiv - QuantFin - Trading and Market Microstructure","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Trading and Market Microstructure","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.18177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent
a widely used class of automated market makers (AMMs). These G3Ms are
characterized by the following rule: the reserves of the AMM must maintain the
same (weighted) geometric mean before and after each trade. This paper
investigates the effects of trading fees on liquidity providers' (LP)
profitability in a G3M, as well as the adverse selection faced by LPs due to
arbitrage activities involving a reference market. Our work expands the model
described in previous studies for G3Ms, integrating transaction fees and
continuous-time arbitrage into the analysis. Within this context, we analyze
G3M dynamics, characterized by stochastic storage processes, and calculate the
growth rate of LP wealth. In particular, our results align with and extend the
results concerning the constant product market maker, commonly referred to as
Uniswap v2.
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